This is a blog of essays on public policy. It shuns ideology and applies facts, logic and math to economic, social and political problems. It has a subject-matter index, a list of recent posts, and permalinks at the ends of posts. Comments are moderated and may take time to appear. Note: Profile updated 4/7/12

06 March 2013

Solar Car Payback

[For a recent post on our global moral crisis, click here. Sorry to upstage it, but energy trumps morals, as it always has and always will.]
By installing a solar photovoltaic array for your home or business, you can cut your electric bill. If your power company offers net metering, you will save the cost you would otherwise pay for every kilowatt-hour of energy your array generates.
If your array generates excess energy (more than you use), you may also receive a credit for each kilowatt-hour that the array produces that you don’t use. Usually, that excess-energy credit is at a lower rate, fixed more by politics than economics. (Most power companies also limit the amount of excess energy that they have to pay for. After all, they do tend to capture the public utility commissions that are supposed to regulate them.)
Together, your savings and any so-called “rec credit” for excess energy determine your “payback period,” that is, how long the array has to run before its savings and earnings have repaid its initial fixed cost. Thereafter, the power your array generates is free, and any excess power gives you extra income.
But suppose you install a solar photovoltaic array not to power your home or business, but to power one or more electric cars. Then your savings per kilowatt-hour are much higher. Why? Because you save not just the cost per kilowatt-hour that you would otherwise pay for electric energy, but the higher energy cost of gasoline.
How much higher? It’s easy to make an accurate estimate. Suppose you have a small car, comparable in size to an electric car. Say it gets 30 miles to the gallon, and gasoline costs $3.60 a gallon. That works out to 12 cents a mile.
Now suppose you had a Nissan Leaf instead. The EPA rates its range as 73 miles per charge, and its battery holds 24 kilowatt-hours of energy [scroll to “Cell Power”]. That works out to almost exactly three miles per kilowatt-hour. So for each kilowatt-hour of electric driving, you would save three-miles worth of gasoline, or 36 cents by our estimate above. That’s over three times the savings of the price of electricity at the national average residential retail price for 2012 (11.88 cents per kilowatt-hour).
As compared to lower electric rates, the gasoline-cost multiplier is even higher. For example, the 36-cents-per-kilowatt-hour-equivalent is over five times the national average cost of industrial electric power for 2012, namely, 6.70 cents per kilowatt-hour.
These large differences between the energy cost of gasoline and the average cost of electricity make payback periods particularly attractive for solar arrays used to charge electric cars.
The following table shows the payback periods in years for solar arrays used only to charge electric cars, assuming the present 30% federal tax credit and an additional 10% tax credit (as in New Mexico) for the array expense:

Payback Periods for Solar-Driving Arrays

Mfg Cost Mof 1 W cell

Turnkey Factor T

Payback Period

cents

(dimensionless)

years

100

6

8.57

100

3

4.2

50

6

4.2

50

3

2.1

This table assumes a nominal array power of three kilowatts per car—sufficient to charge a Leaf’s 24-kilowatt-hour battery in eight hours. It assumes that each electric car runs fifty miles every weekday of the year (a total of 210 days), for a total annual mileage of 10,500. Finally, it assumes the same 2,000 hours of useful array operation per year derived in my previous post, which also explains the array cost parameters M and T.
The car’s assumed operation, less than two days out of three (210 weekdays per year), comports with our previous reasonable assumptions about the availability of useful solar radiance. Net metering eliminates the intermittency issue and accounts for the fact that the cars charge at night. In fact, charging them at night while producing net power during the day actually facilitates grid management because other loads (such as air conditioning, industry, and interior lighting of offices) are heavier during daytime.
With these reasonable assumptions, the payback period in years is the 3-kW array construction cost 3,000MT, in cents, reduced by the total 40% tax credit, and divided by the annual gasoline savings, also in cents, thus:

Payback period = 1,800MT/(12 x 10,500) = 0.014 x MT

These short payback periods derive from the high energy cost of gasoline. My own retail solar array, for which I just signed a contract, costs out at an M of 100 and a T of 6. These numbers are not theory; they are fact. So if my array was just for driving, not running my household as well, I could recover its cost in about 8 years, seven months. After that, my driving energy would be absolutely free, except for the small cost of maintaining the solar array.
As solar-cell costs drop to 50 cents per Watt capacity, the payback period drops to a bit over four years. As Turnkey Factors drop as well to 3, for large-scale commercial arrays, the payback period becomes compelling: 4.2 years for Turnkey Factors of 3 or cell capacity costs of 50 cents per Watt, then just over two years for both of these lower parameters. After these short periods, there is no cost for running the cars, other than maintaining them and the solar-array, as long as the array lasts. With projected effective lifetimes well above the half-century mark, the cost advantages of solar driving over gasoline are compelling.
The Cost of Electric Cars
The short payback period for solar-powered driving does not by itself cancel out the initial-cost disadvantage of electric cars. Not quite yet. But it does go a long way toward neutralizing that price disadvantage over the car’s warranted lifetime, let alone its probable useful life.
As of early 2013, Nissan reduced its MSRP for the entry-level Leaf to $28,800. That’s still higher than what a comparably performing gasoline car would cost. But if you have a solar array for power, and if you run the Leaf only 10,500 miles per year, you will save $1,260 per year on gasoline over a 30 MPG gasoline car.
In a mere six years, your savings will have reduced the effective price to $21,240—a respectably low price for a small car for short-range commuting and shopping. And with the Leaf’s eight-year battery warranty, you’ll still have two years left to recover the cost of your solar array.
All this is without any incentives for the car itself. But incentives there are. If you live in California, for example, combined federal and state tax credits can reduce the entry-level Leaf’s price to as low as $18,800. That’s about as little as you can expect to pay for any car that runs reliably. With that price, you can pay back your solar array before the Leaf’s battery warranty runs out, even if you pay today’s high home-retail prices for your solar installation. Then you can power your next electric car absolutely for free, for its entire useful lifetime.
For businesses, the news is even better. If you have a fleet of city runabouts, you might secure the lower Turnkey Factor (3) for commercial solar arrays, and/or the lower M (50 cents per Watt capacity) for recent solar cells. Then you could achieve payback on your solar array in about four years or less, securing energy-cost-free driving for the foreseeable future. You would still have to maintain the vehicles, but maintenance would be much cheaper than for gasoline-driven cars because electric cars are much simpler.
The bottom line is clear. To “go electric,” you have to be willing to plan ahead and work with contractors. But with current federal and state tax credits, cost factors no longer weigh on the decision. You can acquire small, light electric cars for much the same initial outlay as for similar gasoline cars. And with a little extra planning and foresight you can arrange, after a short payback period, to pay nothing at all for their fuel (and much less for maintenance than with gasoline cars) for the foreseeable future.
The era of pollution-free electric driving already has begun. It offers not just freedom from environmental guilt, but also cost savings and personal energy independence.
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About Me

This blog reflects a quarter century of study and forty years of careers in science/engineering (7 years), law practice (8 years) and law teaching (25 years). A short bio and legal publication list appear here. My pre-retirement 2010 CV appears here.
As I get older, I find myself thinking more like an engineer and less like a lawyer or law professor. Our “advocacy” professions—law, politics, public relations and advertising—train people to take a predetermined position and support it against all opposition. That’s not the best way to make things work—which is what engineers do.
What gets me up in the morning is figuring out how things work and how to make them work better, whether they be vehicles, energy systems, governments or nations.
This post explains my respect for math and why you’ll find lots of tables and a few graphs and equations on this blog. If you like that way of thinking, this blog is for you.